I did cry at the ending of PMD : Darkness/Time/Sky. Just- accepting that you're going to be wiped from existence if you succeed, and if you don't, everything goes to chaos.
But this shows a perfect example of the Grandfather Paradox. Simply put, since the future was changed from what it was originally supposed to be, your character - and Grovyle - ceased to exist. But, since your character didn't exist, that means he wouldn't have been able to go back in time and change the future. I don't know; just something to ponder about.
I didn't exactly cry at the end of Red and Blue PMD, but I did feel pretty sad. And what I've seen from giancarloparimango on YouTube, the next PMD games also get those sad parts.

And there's not a whole lot of games that have made me shead tears.
I mean, there's - maybe Mother 3, though it was a while ago I first beaten it, Katawa Shoujo, if you consider it to be a game, and Aerith dying - because I was just so unprepared for that.
And maybe some parts of Okami and Okamiden.